Ink-jet printer head and ink-jet printer

ABSTRACT

An ink-jet recording head is capable of always performing high-speed recording with high image quality in a stable manner independently of a change in the environmental temperature while an apparatus is in operation. The configurations of a nozzle  7 , an ink supply aperture  6 , and a pressure generating chamber  2  are set so that an inertance m T  and an acoustic resistance r T  (the values substantially at a temperature of 20° C.) of the nozzle  7 , the ink supply aperture  6 , and the pressure generating chamber  2  in an ink-filled state satisfy expressions (1) and (2), respectively: 
     
       
         0&lt;m T &lt;1.9×10 8 [kg/m 4 ]  (1) 
       
     
     
       
         4.0×10 12 &lt;r T &lt;11.0×10 12 [Ns/m 5 ]  (2)

TECHNICAL FIELD

The present invention relates to an ink-jet recording head adapted todischarge minute ink droplets from a nozzle to record characters orimages, and an ink-jet recording apparatus in which the ink-jetrecording head is installed.

BACKGROUND ART

Hitherto, as one of this type of recording heads, an “on-demand typeink-jet recording head” that discharges ink droplets from a nozzleaccording to printing information has been extensively known, Anon-demand type ink-jet recording head has been disclosed in, forexample, Japanese Examined Patent Publication (JP-B) No. 53-12138. FIG.11 is a sectional view that conceptually shows a basic construction ofan ink-jet recording head known as a Caesar type among the on-demandtype ink-jet recording heads.

As shown in FIG. 11, in the Caesar type recording head, a pressuregenerating chamber 91 and a common ink chamber 92 are coupled via an inksupply aperture (ink supply passage) 93 at an ink upstream side. At anink downstream side, the pressure generating chamber 91 and a nozzle 94are coupled. A bottom plate of the pressure generating chamber 91 shownin the drawing is composed of a diaphragm 95, and a piezoelectricactuator 96 is provided on the rear surface of the diaphragm 95.

In such a construction, to perform a printing operation, thepiezoelectric actuator 96 is driven to displace the diaphragm 95 on thebasis of printing information, thereby suddenly changing the volume ofthe pressure generating chamber 91 to produce a pressure wave in thepressure generating chamber 91. The pressure wave causes a part of theink charged in the pressure generating chamber 91 to be injected outsidethrough the nozzle 94 in the form of an ink droplet 97. The dischargedink droplet 98 impacts onto a recording medium, such as recording paper,and forms a recording dot. Such a recording dot is repeatedly formed onthe basis of the printing information thereby to record a character oran image on the recording medium.

Referring now to FIGS. 12(a) through (d) and FIG. 13, the relativitybetween the behaviors of a meniscus and printing performance will bediscussed.

FIGS. 12(a) through (d) are sectional views illustrating a changingprocess of a meniscus M of the nozzle 94 in the aforesaid ink dropletdischarging process, and FIG. 13 is a graph showing time-dependentchanges of the position of the meniscus M after the ink droplet isdischarged. Before the ink droplet 97 is discharged, the meniscus M isset so that it is positioned substantially flush with an aperturesurface of the nozzle 94, as shown in FIG. 12(a). When the piezoelectricactuator 96 is driven and the ink droplet 97 is discharged, the meniscusM moves back into the nozzle 94 according to the amount of thedischarged ink, as shown in FIG. 12(b). At this time, if the nextdischarge is implemented while the meniscus M is still back in thenozzle 94, as shown in FIG. 12(c), then a discharging condition (adroplet diameter, droplet speed, etc.) changes, or a discharge failureresults. Hence, in order to achieve stable continuous discharge, it isimportant to wait until the meniscus M that has retreated is moved backto the vicinity of its initial position by the action of surfacetension, as illustrated in FIG. 12(d), before the next discharge cycleis implemented. More specifically, it is crucial to start the nextdischarge cycle after a time required for refilling after the ink isdischarge has elapsed (refilling time t_(r)), as shown in FIG. 13.

From the descriptions above, it can be understood that a maximumdischarging frequency fe of the ink-jet recording head depends on therefilling time t_(r) of the head. More specifically, to attainhigh-speed recording by operating at the maximum discharging frequencyfe, it is necessary to shorten the refilling time t_(r) so as to satisfya condition indicated by t_(r)<1/fe. To be more specific, the refillingtime t_(r) can be reduced by increasing a cross-sectional area of thepassage system formed of the nozzle 94, the pressure generating chamber93, and the ink supply aperture (ink supply passage) 91, or bydecreasing the viscosity of the ink thereby to decrease a passageresistance.

However, reducing the passage resistance results in a side effect of anincrease in an overshoot X_(max) of the meniscus M, as shown in FIG. 13,although the refilling time t_(r) is shortened. More specifically, ifthe overshoot X_(max) is large, then the condition (position or speed)of the meniscus M immediately before the discharge of the ink droplet 97does not remain constant, leading to an inconvenient problem in that thedroplet diameter or the droplet speed (discharging speed) of the droplet97 varies. Therefore, to secure the accuracy in the droplet diameter orthe droplet speed, it is required to control the overshoot X_(max) ofthe meniscus M to a predetermined value or less. Especially toaccomplish recording with high image quality by droplet diametermodulation, high accuracy is required of the droplet diameter and thedroplet speed. For this reason, the overshoot amount X_(max) must beapproximately 10 μm at maximum. A specific measure for suppressing theovershoot X_(max), the cross-sectional area of the passage system may bereduced or the ink viscosity may be increased so as to increase thepassage resistance. As mentioned above, however, increasing the passageresistance causes the refilling time t_(r) to be prolonged, so thathigh-speed recording is inconveniently sacrificed.

Thus, in the ink-jet recording head, it is extremely difficult torealize the recording with high image quality performed by dropletdiameter modulation, and also high-speed recording at the same time,because the conflicting conditions, namely, the shortened refilling timet_(r) and the restrained overshoot X_(max) must be satisfied. In thepast, however, attempts have been made to realize both the recordingwith high image quality and high-speed recording by maximizing thereduction in the refilling time and the restraint of the overshoot bydevising the shapes of the nozzle or ink supply aperture (the ink supplypassage) or the like, and by adjusting the viscosity of the ink.

According to the conventional attempts mentioned above, however, it hasbeen extremely difficult to always achieve the shortened refilling timeand the restrained overshoot over a wide operating temperature range ofthe apparatus. This is because the physical properties of the ink changedue to environmental temperatures, and as a result, refillingcharacteristics markedly change.

As it will be discussed hereinafter, the refilling characteristics ofthe ink-jet recording head are governed by the inertance (acoustic mass)and the acoustic resistance of the passage system formed of a nozzle, anink supply aperture (an ink supply passage), a pressure generatingchamber, etc., and the acoustic capacitance of a meniscus. Among thesefactors, the inertance depends on the density of ink, the acousticresistance depends on the viscosity of ink, and the acoustic capacitancedepends on the surface tension of ink. Therefore, if the ink properties(density, viscosity, and surface tension) change according toenvironmental temperatures, then the characteristic parameters(inertance, acoustic resistance, and acoustic capacitance) of a passagesystem change accordingly, resulting in a significant change in therefilling characteristics. Actually, when the operating temperaturerange of the apparatus is 10 to 35° C. (in the vicinity of roomtemperature), the dependence-on-temperature of the density and thesurface tension can be almost ignored, but the temperature-dependentchange of the ink viscosity cannot be ignored.

For instance, if the operating temperature of the apparatus is set to 10to 35° C., then the ink viscosity of a typical water-based ink developsan approximately 2.0-fold to 2.5-fold change. If the environmentaltemperature is low, then the ink viscosity increases with a resultantincrease in the acoustic resistance of the passage system, making itdifficult to obtain a desired refilling time t_(r). Conversely, if theenvironmental temperature rises, then the ink viscosity decreases, sothat the overshoot X_(max) of the meniscus increases although therefilling time t_(r) shortens.

As a specific example, an example of a result of an experiment on anink-jet recording head will be described. At room temperature (20° C.),the refilling time t_(r) was 90 μs, and the overshoot X_(max) r, was 5μm. In the ink-jet recording head, a target drive frequency is 10 kHz,and the allowable value of the overshoot X_(max) is 10 μm at this time.Hence, at the room temperature (20° C.), the target value (100 μs orless) of the refilling time t_(r) can be secured, and the overshootX_(max) can be restrained. However, when the environmental temperaturewas lowered to 10° C., then the overshoot X_(max) was decreased to 2 μmand therefore satisfied the overshoot condition, whereas the refillingtime increased to t_(r) 116 μs, so that it was no longer possible tosecure the target refilling time t_(r). Conversely, when theenvironmental temperature was increased to 35° C., the refilling timet_(r) was shortened to 72 μs and therefore satisfied the refilling timecondition, whereas the overshoot increased to 14 μm, indicating that itwas no longer possible to restrain the overshoot X_(max).

As described in detail above, since the ink viscosity greatly depends ontemperature, it is extremely difficult to secure a target refilling timeand to restrain the overshoot at the same time over a wide apparatusoperating temperature range. Especially when the diameter of inkdroplets to be discharged is set to a larger value so as to realizehigh-speed recording, marked deterioration is observed in the printingperformance attributable to the temperature-dependent changes in thephysical properties of ink. For example, when the recording resolutionis set to a low value, approximately 400 dpi, the required ink dropletdiameter (maximum droplet diameter) will be about 38 μm to about 43 μm.When such a large ink droplet is discharged, the amount of recession ofa meniscus immediately after the discharge is large. This is likely tocause an increase in the refilling time or the overshoot, and also leadsto increased susceptibility to the influences of the changes inenvironmental temperature. In fact, no ink-jet recording head hasconventionally been available that is capable of perfectly securing therefilling time and restraining the overshoot at the same time under acondition where an ink droplet diameter of a maximum droplet diameter Hzor more, an overshoot allowable value of 10 μm, and the apparatusoperating temperature ranges from 10 to 35° C. In the presentspecification, the droplet diameter means the diameter obtained byconverting the total amount of ink discharged in one discharge cycleinto a single spherical ink droplet.

Accordingly, an object of the present invention is to provide an ink-jetrecording head capable of always securing a target refilling time andrestraining overshoot at the same time even if an environmentaltemperature changes while an apparatus is in operation, and also capableof discharging at high speed a stable ink droplet with highly accuratedroplet diameter and droplet speed. It is another object of theinvention to provide an ink-jet recording apparatus in which theaforesaid head is installed.

DISCLOSURE OF THE INVENTION

To this end, the invention described in claim 1 relates to an ink-jetrecording head that includes a pressure generating chamber filled withink, pressure generating means for generating a pressure in the pressuregenerating chamber, an ink supply chamber for supplying the ink to thepressure generating chamber, an ink supply passage for establishingcommunication between the ink supply chamber and the pressure generatingchamber, and a nozzle in communication with the pressure generatingchamber, the pressure generating means causing a pressure change to takeplace in the pressure generating chamber so as to discharge an inkdroplet from the nozzle, wherein the configurations of the nozzle, theink supply passage, and the pressure generating chamber are set so thata total sum m_(T) of the inertance and a total sum r_(T) of acousticresistance (the values at a temperature of about 20° C.) of the nozzle,the ink supply passage, and the pressure generating chamber in anink-filled state satisfy expressions (4) and (5):

0<m_(T)<1.9×10⁸[kg/m⁴]  (4)

4.0×10¹²<r_(T)<11.0×10¹²[Ns/m⁵]  (2)

The invention described in claim 2 relates to the ink-jet recording headdescribed in claim 1, wherein the nozzle has a tapered portion whosediameter gradually increases toward the pressure generating chamber, andthe tapering angle of the tapered portion is 10 to 45 degrees.

The invention described in claim 3 relates to the ink-jet recording headdescribed in claim 1, wherein the nozzle is composed of a straightportion provided in the vicinity of an opening and a tapered portionthat gradually increases toward the pressure generating chamber, and thetapering angle of the tapered portion is 15 to 45 degrees.

The invention described in claim 4 relates to the ink-jet recording headdescribed in claim 1, wherein the diameter of the nozzle graduallyincreases toward the pressure generating chamber, the longitudinalsection of the nozzle is shaped into a curve that has a radiussubstantially equal to the length of the nozzle, and the length of thenozzle is 50 to 100 μm.

The invention described in claim 5 relates to the ink-jet recording headdescribed in claim 1, 2, 3, or 4, wherein the opening diameter of thenozzle is 25 to 32 μm.

The invention described in claim 6 relates to the ink-jet recording headdescribed in claim 1, wherein the ink supply passage is an ink supplyaperture for establishing communication between the ink supply chamberand the pressure generating chamber.

The invention described in claim 7 relates to the ink-jet recording headdescribed in claim 1, wherein the maximum droplet diameter of the inkdroplet is set to 38 to 43 μm.

The invention described in claim 8 relates to the ink-jet recording headdescribed in claim 1, wherein the ink-jet recording head employs an inkwith its surface tension set to 25 to 35 mN/m.

The invention described in claim 9 relates to the ink-jet recording headdescribed in claim 1, wherein the ink-jet recording head employs an inkhaving its viscosity set such that the total sum r_(T) of the acousticresistance (the value at a temperature of substantially 20° C.) of thenozzle, the ink supply passage, and the pressure generating chamber inan ink-filled state satisfies expression (6):

4.0×10¹²<r_(T)<11.0×10¹²[Ns/m⁵]  (6)

The invention described in claim 10 relates to an ink-jet recordingapparatus incorporating the ink-jet recording head described in any oneof claims 1 to 9.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1(a) is a sectional view conceptually showing the construction ofan ink-jet recording head used in a first embodiment of the presentinvention;

FIG. 1(b) is an exploded sectional view showing the ink-jet recordinghead in a disassembled state;

FIG. 2 is a block diagram showing an electrical configuration of anon-modulated droplet diameter type driving circuit that drives theink-jet recording head in a binary mode;

FIG. 3 is a block diagram showing an electrical configuration of amodulated droplet diameter type driving circuit that drives the ink-jetrecording head in a multi-gray-scale mode;

FIG. 4 is a sectional view showing the shape of a nozzle constitutingthe ink-jet recording head (an ink supply aperture has the same shape);

FIG. 5 is a graph showing the relationship between an inertance m_(T)and an acoustic resistance r_(T) of an entire passage diameter in theembodiment;

FIG. 6 is a graph showing the relationship between an inertance m_(T)and an acoustic resistance r_(T) of an entire passage diameter in theembodiment;

FIG. 7 is a sectional view showing the shape of a nozzle (an ink supplyaperture has the same shape) that is a second embodiment of the presentinvention;

FIG. 8 is a sectional view showing the shape of a nozzle (an ink supplyaperture has the same shape) that is a third embodiment of the presentinvention;

FIG. 9 is a diagram for explaining the theoretical validity of thepresent invention, and is an equivalent circuit diagram of an ink-jetrecording head in a refilling operation;

FIG. 10 is a diagram for explaining the theoretical validity of thepresent invention, and is a graph showing the relationship between aninertance m_(T) and an acoustic resistance r_(T) of an entire passagediameter;

FIG. 11 is a diagram for explaining a conventional technology, and is asectional view conceptually showing the basic construction of an ink-jetrecording head known as a Caesar type among on-demand type ink-jetrecording heads;

FIGS. 12(a) through (d) are diagrams for explaining the conventionaltechnology, and are sectional views showing how the meniscus of a nozzlechanges in the aforesaid ink droplet discharging process; and

FIG. 13 is a diagram for explaining a prior art, and shows thetime-dependent changes of the position of the meniscus after an inkdroplet is discharged.

BEST MODE EMBODYING THE INVENTION

Referring now to the drawings, the embodiments of the present inventionwill be described.

To help better understand the present invention, the theoreticalfoundation of the validity of the present invention will be firstexplained by using a concentrated constant system equivalent circuitmodel.

FIG. 9 is an equivalent circuit diagram showing an ink-jet recordinghead in a refilling operation. From the equivalent circuit, it isunderstood that the meniscus movement in the refilling operation isgoverned by the differential equation of expression (7): $\begin{matrix}{m_{T} = {{\frac{^{2}x}{t^{2}} + {r_{T}\frac{x}{t}} + {\frac{1}{c_{3}}x}} = 0}} & (7)\end{matrix}$

In expression (7), m_(T) denotes a total sum of the inertance (acousticmass) of a nozzle, an ink supply passage, and a pressure generatingchamber in an ink-filled state. An inertance m in each component isdetermined by expression (8) when a conduit sectional area is denoted asS [m2], a conduit length is denoted as I [m], and an ink density isdenoted as p [kg/m³]: $\begin{matrix}{m = {\int_{o}^{l}{\frac{\rho}{s}{x}}}} & (8)\end{matrix}$

In expression (7), r_(T) denotes the total sum of the acousticresistances of the nozzle, the ink supply passage, and the pressuregenerating chamber in the ink-filled state. An acoustic resistance r ineach component at a portion, where the conduit section is round, isdetermined by expression (9) when the ink viscosity is denoted as η[Pa·s] and the conduit diameter is denoted as d [m]. At a portion wherethe conduit section is rectangular, the acoustic resistance r isdetermined by expression (10) when the aspect ratio (the slendernessratio) of the section is denoted as z: $\begin{matrix}{r = {\int_{o}^{l}{\frac{128\eta}{\pi \quad d^{4}}{x}}}} & (9) \\{r = {\int_{o}^{l}{\frac{12\eta \quad l}{s^{2}}{x}\left\{ {0.33 \times 1.02\left( {z + \frac{1}{z}} \right)} \right\}}}} & (10)\end{matrix}$

In expression (7), C3 denotes the acoustic capacitance [m⁵/N] of ameniscus, and is determined by expression (11) when a nozzle openingdiameter is denoted as d₃ [m], the surface tension of ink is denoted asσ [N/m], and the recession of the meniscus is denoted as x [m]:$\begin{matrix}{c_{3} = {\frac{\pi \quad d_{3}^{4}}{64\rho}\sqrt{1 + \frac{16x^{2}}{d_{3}^{2}}}}} & (11)\end{matrix}$

To determine the time-dependent changes of the position of the meniscusfrom expression (7), it is required to give an initial position x₀ ofthe meniscus at the start of refilling (refer to FIG. 12(b) and FIG.13). When the droplet diameter is denoted as d_(d) [m], the initialposition x₀ of the meniscus is given by expression (12). A coefficient κnormally takes a value of about 0.5 to about 0.7 although it somewhatchanges, depending upon the shape of the nozzle, or the like. Incalculation performed primarily by the inventor related to the presentapplication, the coefficient was set to κ=0.67 based on the result ofexperiments. $\begin{matrix}{x_{0} = {\kappa \frac{_{d}^{3}}{_{3}^{2}}}} & (12)\end{matrix}$

As can be understood from expression (7) through expression (12), oncethe nozzle opening diameter d₃ (FIG. 12(a)), the surface tension σ ofthe ink, and the droplet diameter d_(d) of the ink are determined, thereare only two parameters that govern the refilling operation, namely, theinertance m_(T) and the acoustic resistance r_(T). In other words, thecombination of the inertance m_(T) and the acoustic resistance r_(T)decides the refilling characteristics (refilling time and overshootamount). In this case, setting the inertance m_(T) at a certain valuewill determine the upper limit of the acoustic resistance r_(T) forattaining a target refilling time and the lower limit of the acousticresistance r_(T) for controlling the overshoot amount to an allowablevalue or less. An actual example is illustrated in the graph shown inFIG. 10 (calculated under a condition where d₃=30 μm, σ=33 mN/m,d_(d)=40 μm, and the discharge frequency fe=10 kHz). The graph shown inFIG. 10 plots the upper/lower limits of the acoustic resistance r_(T)corresponding to each inertance m_(T) when the inertance m_(T) ischanged within the range of 0.5 to 4.5×10⁸ kg/m⁴.

In FIG. 10, plotting indicated by □ shows the upper limit of theacoustic resistance r_(T) for securing a target refilling time (100 μs).If the acoustic resistance r_(T) exceeds the upper limit, then a targetdischarge frequency cannot be obtained. Plotting indicated by ♦ showsthe lower limit of the acoustic resistance r_(T) for controlling theovershoot amount to the allowable value (10 μm) or less. Hence, it willbe possible to secure the target refilling time and to restrain theovershoot at the same time by setting the inertance m_(T) and theacoustic resistance r_(T) such that the acoustic resistance r_(T) stayswithin the range defined by the upper limit and the lower limit (thehatched area).

For instance, in an ink-jet recording head, it is assumed that thecombination of the inertance m_(T) and the acoustic resistance r_(T)(calculated using an ink viscosity of 2.9 mPa·s at 20° C.) lies at theposition indicated by plotting denoted by O shown in FIG. 10 when theenvironmental temperature is room temperature (20° C.). At theenvironmental temperature of the room temperature (20° C.), the acousticresistance r_(T) lies between the upper limit and the lower limit, sothat the target refilling time can be secured and the overshoot can berestrained at the same time. However, if the environmental temperaturechanges in the range of 10 to 35° C., then the ink viscosity η changesin the range of 1.8 to 3.8 mPa·s. This causes the acoustic resistancer_(T) to change in the range defined by the arrows in FIG. 10. Thismeans that, at a lower temperature, the acoustic resistance r_(T)exceeds the upper limit, so that refilling time will exceed the target.At a higher temperature, the acoustic resistance r_(T) exceeds the lowerlimit, so that the overshoot amount will exceed the allowable value. Inother words, the ink-jet recording head has a head structure that cannotsuccessfully cope with the changes in environmental temperature.

Another ink-jet recording head will be discussed. In this head, thecombination of the inertance m_(T) and the acoustic resistance r_(T)lies at the position indicated by plotting denoted by Δ shown in FIG. 10when the environmental temperature is the room temperature (20° C.). Asis obvious from FIG. 10, this ink-jet recording head always staysbetween the upper limit and the lower limit even if the environmentaltemperature changes in the range of 10 to 35° C. Therefore, this head isable to always secure a target refilling time and restrain overshoot atthe same time within the range of 10 to 35° C., and is accordingly ableto successfully cope with changes in environmental temperature. In otherwords, to enable an ink-jet recording head to successfully deal withchanges in environmental temperature, it is crucial to set the inertancem_(T) and the acoustic resistance r_(T) such that the acousticresistance r_(T) is always positioned between the upper limit and thelower limit within an apparatus operating temperature range.

Conventionally, however, a design concept based on the viewpoint ofoptimized balance between the inertance m_(T) and the acousticresistance r_(T) has not been known, For this reason, according to theanalytical results obtained primarily by the inventor of the presentapplication, no head is available that is designed to have an inkdroplet diameter set to 38 to 43 μm, and the acoustic resistance r_(T)always lies within a permissible range (the area between an upper limitvalue and a lower limit value) over the full range of environmentaltemperatures from 10 to 35° C.

As can be understood from expression (7) to expression (12), theallowable range of the inertance m_(T) and the acoustic resistance r_(T)is inherently represented as a function that depends on five parameters,namely, the ink droplet diameter d_(d), the nozzle opening diameter d₃,the surface tension a of ink, a maximum discharge frequency, and anallowable overshoot value. However, the present invention covers a largedroplet in a low-resolution recording operation (approximately 400 dpi)wherein the influences of an environmental temperature is particularlymarked. Therefore, the allowable range of the inertance m_(T) and theacoustic resistance r_(T) can be numerically specified as describedbelow.

Specifically, when the maximum discharge frequency is set to 10 kHzM andthe allowable overshoot value is set to 10 μm, largest optimum values ofthe higher limit value of the inertance m_(T) and the acousticresistance r_(T) in the range to which the present invention applies(the maximum droplet diameter of an ink droplet d_(d)=38 to 43 μm, thenozzle opening diameter d₃=25 to 32 μm, and the surface tension of inkσ=25 to 35 mN/m) are obtained when the ink droplet diameter is d_(d)=38μm, the nozzle opening diameter is d₃=25 μm, and the surface tension ofink is σ=35 mN/m. If the changing range of environmental temperature isabout 10 to about 35° C., then the desirable upper limit value of theinertance m_(T) will be about 1.9×10⁸kg/m⁴, and the allowable range ofthe acoustic resistance r_(T) (20° C.) will be9.0×10¹²<r_(T)<11.0×10¹²[Ns/m]. Conversely, smallest optimum values ofthe upper limit value of the inertance m_(T) and T of the acousticresistance r are obtained when the ink droplet diameter is d_(d)=43 μm,the nozzle opening diameter is d₃=32 μm, and the surface tension of inkis σ=28 mN/m. At this time, the upper limit value of the inertance m_(T)will be about 0.9×10⁸kg/m⁴, and the allowable range of the acousticresistance r_(T) (20° C.) will be 4.0×10¹²<r_(T)<5.0×10¹²[Ns/m⁵].

Accordingly, in the ink-jet recording head, which has been set to therange covered by the present invention (the maximum droplet diameter ofan ink droplet is d_(d)=38 to 43 μm, the nozzle opening diameter isd₃=25 to 32 μm, and the surface tension of ink is σ=25 to 35 mN/m), inorder to realize a maximum discharge frequency of 10 kHz or more and anallowable overshoot value of 10 μm over the entire environmentaltemperature range of about 10 to about 35° C., at least the conditionsof expressions (13) and (14) must be satisfied:

0<m_(T)<1.9×10⁸[kg/m⁴]  (13)

4.0×10¹²<r_(T)<11.0×10¹²[Ns/m⁵]  (14)

The specific embodiments of the present invention will now be explained.

FIRST EMBODIMENT

FIG. 1(a) is a sectional view conceptually showing the construction ofan ink-jet recording head mounted on an ink-Jet recording apparatuswhich is a first embodiment of the present invention, FIG. 1(b) is anexploded sectional view showing the ink-jet recording head in adisassembled state, FIG. 2 is a block diagram showing an electricalconfiguration of a non-modulated droplet diameter type driving circuitthat drives the ink-jet recording head, and FIG. 3 is a block diagramshowing an electrical configuration of a modulated droplet diameter typedriving circuit that drives the ink-jet recording head.

The ink-jet recording head of this example is, as shown in FIG. 1(a), anon-demand Caesar type multi-nozzle recording head that discharges, asnecessary, an ink droplet 1 to print a character or image on recordingpaper. As shown in FIG. 1(a), the recording head is primarilyconstituted by a plurality of pressure generating chambers 2 that areindividually formed in long and slender cubic shapes and arrangedvertically in the drawing, a diaphragm 3 making up the bottom surface ofeach of the pressure generating chambers 2 in the drawing, a pluralityof piezoelectric actuators 4 that are provided side by side on the rearsurfaces of the diaphragms 3 to match the pressure generating chambers 2and are composed of laminated piezoelectric ceramics, a common inkchamber (ink pool) 5 coupled to an ink tank, which is not shown, tosupply ink to the pressure generating chambers 2, a plurality of inksupply apertures (communication apertures) 6 for establishing one-to-onecommunication between the common ink chamber 5 and the pressuregenerating chambers 2, and a plurality of nozzles 7 that are provided tobe keyed one-to-one to the pressure generating chambers 2, and dischargethe ink droplet 1 from the distal ends projecting at the tops of thepressure generating chambers 2. The common ink chamber 5, the ink supplypassages 6, the pressure generating chambers 2, and the nozzles 7 makeup a passage system in which ink moves in this order. The piezoelectricactuators 4 and the diaphragms 3 make up a vibration system for applyinga pressure wave to the ink in the pressure generating chambers 2. Thecontact points of the passage system and the vibration system providethe bottom surfaces of the pressure generating chambers 2 (i.e., the topsurfaces of the diaphragms 3 in the drawing).

In the head manufacturing process of this embodiment, as shown in FIG.1(b), a nozzle plate 7 a in which the plurality of nozzles 7 arearranged and opened in columns or in a zigzag pattern, a pool plate 5 ain which a space portion of the common ink chamber 5 is formed, a supplyaperture plate 6 a in which an ink supply aperture 6 is drilled, apressure generating chamber plate 2 a in which a plurality of spaceportions of the plurality of pressure generating chambers 2 are formed,and vibrating plates 3 a constituting the plurality of diaphragms 3 areprepared in advance. Thereafter, these plates 2 a, 3 a, and 5 a through7 a are adhesively bonded using an epoxy-based adhesive agent layerhaving a thickness of approximately 20 μm, not shown, to make alaminated plate. Then, the prepared laminated plate and thepiezoelectric actuator 4 are bonded using an epoxy-based adhesive agentlayer thereby to fabricate the ink-jet recording head having theaforesaid construction. In this example, a nickel plate that is producedby electrocasting (electroforming) and has a thickness of 50 to 75 μm isused for the vibrating plate 3 a, while a stainless plate having athickness of 50 to 75 μm is used for the other plates 2 a and 5 athrough 7 a.

Referring now to FIG. 2 and FIG. 3, the descriptions will be given ofthe electrical configuration of a driving circuit that constitutes theink-jet recording apparatus of this example, and drives the ink-jetrecording head having the aforesaid construction.

The ink-jet recording apparatus of this example has a CPU (centralprocessing unit) and memories, such as a ROM and RAM, which are notshown. The CPU controls the components of the apparatus by executing aprogram stored in the ROM and employing diverse registers and flagssecured in the RAM to print characters or images on recording paper onthe basis of printing information supplied from a host apparatus, suchas a personal computer, through an interface.

First, the driving circuit shown in FIG. 2 produces and power-amplifiesa predetermined driving waveform signal, then supplies the signal topredetermined piezoelectric actuators 4, 4, . . . associated with theprinting information to drive the actuators so as to discharge the inkdroplet 1, which always has substantially the same droplet diameter, toprint a character or an image on the recording paper. The drivingcircuit is constituted primarily by a waveform generating circuit 21, apower amplifier circuit 22, and a plurality of switching circuits 23,23, . . . connected to the piezoelectric actuators 4, 4, . . . in aone-to-one fashion.

The waveform generating circuit 21 is formed by a digital-to-analogconverting circuit and an integrating circuit, and converts the drivingwaveform data read from a predetermined storage area of the ROM by theCPU into analog data, then performs integration on the analog data togenerate a driving waveform signal. The power amplifier circuit 22power-amplifies the driving waveform signal supplied from the waveformgenerating circuit 21, and outputs the amplified driving waveform signalas a voltage waveform signal. The switching circuit 23 has its input endconnected to an output end of the power amplifier circuit 22, and itsoutput end connected to one end of the associated piezoelectric actuator4. Application of a control signal associated with printing informationoutput from the driving control circuit, not shown, to its control endcauses the switching circuit 23 to be turned ON so as to apply a voltagewaveform signal output from the associated power amplifier circuit 22 tothe piezoelectric actuator 4. At this time, the piezoelectric actuator 4causes the diaphragm 3 to be displaced on the basis of the appliedvoltage waveform signal. The displacement of the diaphragm 3 causes achange in the volume of the pressure generating chamber 2 so as togenerate a predetermined pressure wave in the pressure generatingchamber 2 filled with ink, and the ink droplet 1 of a predetermineddroplet diameter is discharged from the nozzle 7 by the pressure wave.The discharged ink droplet impacts onto a recording medium, such asrecording paper, to form a recording dot. Such a recording dot isrepeatedly formed on the basis of the printing information thereby toform a character or an image on the recording paper in the binary mode.

The driving circuit shown in FIG. 3 is a droplet-diameter-modulatingtype driving circuit adapted to change the diameter of the ink dropletdischarge from the nozzle in multiple steps (in three steps, namely, alarge droplet having a droplet diameter of about 40 μm, a medium dropletof about 30 μm, and a small droplet of about 20 μm in this example) toprint characters or images on recording paper in multiple gray scales.The driving circuit is formed primarily by three types of waveformgenerating circuits 31 a, 31 b, and 31 c for different dropletdiameters, power amplifier circuits 32 a, 32 b, and 32 c connected tothese waveform generating circuits 31 a, 31 b, and 31 c, respectively,in the one-to-one fashion, and a plurality of switching circuits 33, 33,. . . connected to the piezoelectric actuators 4, 4, . . . in theone-to-one fashion.

Each of the waveform generating circuits 31 a through 31 c is composedof a digital-to-analog converting circuit and an integrating circuit. Ofthe waveform generating circuits 31 a through 31 c, the waveformgenerating circuit 31 a converts the driving waveform data fordischarging large droplets read from a predetermined storage area of theROM by the CPU into analog data, and carries out integration on the datato produce the driving waveform signal for discharging large droplets.The waveform generating circuit 31 b converts the driving waveform datafor discharging medium droplets read from a predetermined storage areaof the ROM by the CPU into analog data, and carries out integration onthe data to produce the driving waveform signal for discharging mediumdroplets. The waveform generating circuit 31 c converts the drivingwaveform data for discharging small droplets read from a predeterminedstorage area of the ROM by the CPU into analog data, and carries outintegration on the data to produce the driving waveform signal fordischarging small droplets. The power amplifying circuit 32 apower-amplifies the driving waveform signal for discharging largedroplets supplied from the waveform generating circuit 31 a, and outputsthe amplified signal as a voltage waveform signal for discharging largedroplets. The power amplifying circuit 32 b power-amplifies the drivingwaveform signal for discharging medium droplets supplied from thewaveform generating circuit 31 b, and outputs the amplified signal as avoltage waveform signal for discharging medium droplets. The poweramplifying circuit 32 c power-amplifies the driving waveform signal fordischarging small droplets supplied from the waveform generating circuit31 c, and outputs the amplified signal as a voltage waveform signal fordischarging small droplets,

The switching circuit 33 is composed of first, second, and thirdtransfer gates, not shown. An input end of the first transfer gate isconnected to an output end of the power amplifier circuit 32 a, an inputend of the second transfer gate is connected to an output end of thepower amplifier circuit 32 b, and an input end of the third transfergate is connected to an output end of the power amplifier circuit 32 c.Output ends of the first, second, and third transfer gates are connectedto one end of a corresponding common piezoelectric actuator 4. When agray scale control signal based on the printing information output froma driving control circuit, not shown, is input to a control end of thefirst transfer gate, the first transfer gate is turned ON to apply thevoltage waveform signal for discharging a large droplet, which is outputfrom the power amplifier circuit 32 a, to the piezoelectric actuator 4.At this time, the piezoelectric actuator 4 supplies a displacement basedon the applied voltage waveform signal to the diaphragm 3 so as to causea sudden change (increase or decrease) in the volume of the pressuregenerating chamber 2 by the displacement of the diaphragm 3. This causesa predetermined pressure wave to be produced in the pressure generatingchamber 2 filled with ink thereby to discharge the ink droplet 1 of alarge size from the nozzle 7 by the pressure wave. When a gray scalecontrol signal based on the printing information output from a drivingcontrol circuit is input to a control end of the second transfer gate,the second transfer gate is turned ON to apply the voltage waveformsignal for discharging a medium droplet, which is output from the poweramplifier circuit 32 b, to the piezoelectric actuator 4. At this time,the piezoelectric actuator 4 supplies a displacement based on theapplied voltage waveform signal to the diaphragm 3 so as to change thevolume of the pressure generating chamber 2 by the displacement of thediaphragm 3. This causes a predetermined pressure wave to be produced inthe pressure generating chamber 2 filled with ink thereby to dischargethe ink droplet 1 of a medium size from the nozzle 7 by the pressurewave. When a gray scale control signal based on the printing informationoutput from a driving control circuit is input to a control end of thethird transfer gate, the third transfer gate is turned ON to apply thevoltage waveform signal for discharging a small droplet, which is outputfrom the power amplifier circuit 32 c, to the piezoelectric actuator 4.At this time, the piezoelectric actuator 4 supplies a displacement basedon the applied voltage waveform signal to the diaphragm 3 so as tochange the volume of the pressure generating chamber 2 by thedisplacement of the diaphragm 3. This causes a predetermined pressurewave to be produced in the pressure generating chamber 2 filled with inkthereby to discharge the ink droplet 1 of a small size from the nozzle 7by the pressure wave. The discharged ink droplet impacts onto arecording medium, such as recording paper, to form a recording dot. Suchrecording dots are repeatedly formed on the basis of printinginformation so as to record characters or images in multiple gray scaleson recording paper.

In this embodiment, the ink-jet recording apparatus exclusively used forbinary recording incorporates the driving circuit shown in FIG. 2, whilethe ink-jet recording apparatus that also performs gray-scale recordingincorporates the driving circuit shown in FIG. 3.

FIG. 4 is a sectional view showing the shape of the nozzle 7 in thisembodiment (the ink supply aperture 6 shares the same shape). FIG. 5 andFIG. 6 show the graphs illustrating the relationship between theinertance m_(T) and the acoustic resistance r_(T) of the entire passagediameter in the embodiment. FIG. 6 shows a graph based on the one shownin FIG. 5, wherein the axis of ordinates indicates the ratio of theupper limit and the lower limit of the acoustic resistance r_(T) of theentire passage diameter.

In this case, the inertance m_(T) of the entire passage system means thetotal sum of the inertances of the nozzle 7, the ink supply passage 6,and the pressure generating chamber 2 in the ink-filled state.Similarly, the acoustic resistance of the entire passage diameter meansthe total sum of the acoustic resistances of the nozzle 7, the inksupply passage 6, and the pressure generating chamber 2 in theink-filled state.

The nozzle 7 in this example is formed by punching an aperture byprecision pressing in a stainless plate having a thickness of about 70μm, and formed into a round aperture having an opening diameter of about30 μm. Furthermore, the inner part of the nozzle 7 is tapered to have atapering angle of about 15 degrees, a skirt diameter of about 67 μm, anda length of about 70 μm, as shown in FIG. 4. The ink supply aperture 6shares the same shape with the nozzle 7. In this embodiment, ink isemployed that has been adjusted to have a surface tension of 33 mN/m anda viscosity of 4.5 mPa·s at 20° C. The ink develops about a 2.1-foldchange in the viscosity due to a change in environmental temperature of10 to 35° C.

In the ink-jet recording head in this example, when the environmentaltemperature is the room temperature (20° C.), the combination of theinertance m_(T) and the acoustic resistance r_(T) of the entire headpassage diameter is set such that it lies at the position indicated byplotting O and the total sum r_(T) of the acoustic resistance alwaysstays between the upper limit value and the lower limit value even whenthe environmental temperature changes in the range of 10 to 35° C., asshown in FIG. 5. Hence, as can be understood from FIG. 5, the targetrefilling time (100 μs or less) can be secured, and the overshoot can besuppressed (10 μm or less) at the same time over the entire temperaturerange of 10 to 35° C.

The descriptions will now be given of a specific procedure according towhich the shapes of the nozzle 7 and the ink supply aperture 6, and theviscosity of the ink have been decided as mentioned above.

FIG. 5 shows the results of the determination of the allowable range ofthe acoustic resistance and the inertance m_(T) of the entire passagediameter performed under a condition of a droplet diameter of 40 μm, adischarge frequency of 10 kHz, an allowable overshoot amount of 10 μm,an ink surface tension of 33 mN/m, and a nozzle opening diameter of 30μm. As mentioned above, the ink develops about 2.1-fold viscosity changein response to changes in environmental temperature of 10 to 35° C.Accordingly, the acoustic resistance r_(T) of the entire passagediameter changes 2.1 times due to the changes in the environmentaltemperature of 10 to 35° C. It means, therefore, it the allowable range(the ratio of the upper limit to the lower limit) of the acousticresistance r_(T) of the entire passage diameter cannot accommodate the2.1-fold change, then the apparatus cannot successfully cope withchanges in the environmental temperature. As is obvious from FIG. 6, asthe inertance m_(T) of the entire passage diameter reduces, the ratio ofthe upper limit to the lower limit tends to increase. When the inertanceof the entire passage diameter is m_(T)<1.5×10⁸ kg/m⁴, then the ratio ofthe upper limit to the lower limit is 2.1 or more. Thus, It can beunderstood that the inertance m_(T) of the entire passage diametershould be set to 1.5×10⁸ kg/m⁴ or less to accommodate a 2.1-fold changein the acoustic resistance r_(T) of the entire passage diameter.

Subsequently, the inertance m_(T) of the entire passage diameterdetermined as mentioned above is distributed to the three components,namely, the nozzle 7, the ink supply aperture 6, and the pressuregenerating chamber 2. First, the inertance of the pressure generating 4chamber 2 changes according to the shape of the pressure generatingchamber 2. If an attempt is made to set the maximum ink droplet diameterto 38 to 43 μm and the proper period of a pressure wave to about 10 toabout 20 μs, then the inertance of the pressure generating chamber 2will normally be about 0.4 to about 0.6×10⁸ kg/m⁴. In the case of thisembodiment, the pressure generating chamber 2 is shaped to have a widthof 320 μm, a height of 140 μm, and a length of 2.5 mm. Hence, theinertance of the pressure generating chamber 2 will be 0.56×10⁸ kg/m⁴.Thus, in order to set the inertance m_(T) of the entire passage diameterto 1.5×10⁸ kg/m⁴, it is necessary to set the sum of the inertance of thenozzle 7 and the inertance of the ink supply aperture 6 to 0.94×10⁸kg/m⁴. Since the nozzle 7 and the ink supply aperture 6 substantiallyshare the same shape, the inertance of these two components should besubstantially set to be equal. Therefore, the upper limit value of theinertances of these two components is determined to be 0.47×10⁸ kg/m⁴.

To reduce the inertances of the nozzle 7 and the ink supply aperture 6,it is effective to increase the passage diameter (the passage sectionalarea) and reduce the passage length. However, if the opening diameter ofthe nozzle 7 increases, then adverse influences, such as a drop indroplet speed or deteriorated stability in the discharge of minutedroplets, are likely to take place. For this reason, it is not desirableto considerably increase the opening diameter of the nozzle.Furthermore, if the nozzle length is small, then more air bubbles arelikely to be introduced into the head immediately after discharging.Therefore, it is not desirable to considerably reduce the nozzle length.On the other hand, it has been found that, in order to ensure stabledischarge of ink droplets having a droplet diameter of about 38 to about43 μm at a droplet speed of about 6 to about 10 m/s, the optimum nozzleopening diameter ranges from about 25 to 32 μm and the optimum nozzlelength ranges from about 70 to about 100 μm. To reduce the inertance ofthe nozzle 7 under such a condition, increasing the tapering angle willbe the most effective means. Therefore, in this embodiment, theinertance of the nozzle 7 was brought to a target value, 0.44×10⁸ kg/m⁴,by setting the nozzle diameter to 30 μm, the nozzle length to 70 μm, andthe tapering angle to 15 degrees.

The optimum value of the tapering angle changes according to the nozzlediameter, the nozzle length, the inertance of the pressure generatingchamber, etc. As mentioned above, however, an optimum tapering angle is10 degrees or more, considering that the optimum nozzle opening diameterranges from about 25 to 32 μm, and the optimum nozzle length ranges fromabout 70 to about 100 μm, and it is difficult to significantly increaseor decrease the inertance of the pressure generating chamber 2. However,a tapering angle exceeding 45 degrees is not preferable from theviewpoint of involvement of air bubbles and the strength of nozzle.

In this embodiment, as previously mentioned, the ink supply aperture 6is formed to have the same shape as that of the nozzle 7 so as toprovide the same inertance as that of the nozzle 7.

After completion of setting of the inertance m_(T) of the entire passagediameter, the ink viscosity is set. To be more specific, calculation isperformed to obtain the ink viscosity at the environmental temperatureof 35° C. so that the acoustic resistance r_(T) is set to the lowerlimit value (4.9×10¹² Ns/m⁵) of the acoustic resistance r_(T) at theinertance m_(T)=1.5×10⁸ kg/m⁴. In this embodiment, setting the inkviscosity to 3.0 mPa·s causes the acoustic resistance r_(T) tosubstantially coincide with the lower limit value (4.9×10¹² Ns/m⁵),showing that the viscosity is the optimum ink viscosity at the highesttemperature (35° C.). Thus, the ink viscosity at the lowest temperature(10° C.) will be 2.1 times the viscosity at the highest temperature,that is, 6.3 mPa·s, and the acoustic resistance r_(T) at that time willbe 10.1×10¹² Ns/m⁵. This is the upper limit value or less of theacoustic resistance r_(T), and it is possible to secure the targetrefilling time even at the lowest temperature. In this case, the inkviscosity at the room temperature (20° C.) will be substantially 4.5mPa·s (the viscosity at 20° C. is about 1.5 times the viscosity at 10°C.), and the acoustic resistance r_(T) will be 7.2×10¹² Ns/m⁵.

Thus, by forming the nozzle 7 and the ink supply aperture 6 into a tapershape having a tapering angle of 15 degrees, and setting the inkviscosity substantially to 4.5 mPa·s (20° C.), it is possible to securethe refilling time and also to restrain the overshoot at the same timeover the entire apparatus operating temperature range. The actuallyimplemented evaluation of the refilling characteristics of the ink-jetrecording head according to this embodiment has proven that therefilling time was 98 μs and the overshoot amount was 2.1 μm at thelowest temperature (10° C.), while the refilling time was 64 μs and theovershoot amount was 9.7 μm at the highest temperature (35° C.). Inother words, it has been possible to confirm that the overshoot can becontrolled (10 μm or less) and also to achieve a target drivingfrequency (10 kHz) at the same time over the entire apparatus operatingtemperature range.

SECOND EMBODIMENT

FIG. 7 is a sectional view showing the shape of a nozzle (an ink supplyaperture has the same shape) that is a second embodiment of the presentinvention.

The construction of the second embodiment is significantly differentfrom that of the foregoing first embodiment in that a nozzle 7 a and anink supply aperture 6 a of the second embodiment are provided withstraight portions 71 b and 61 b in the vicinity of their apertures inaddition to tapered portions 71 a and 61 a that gradually increasetoward a pressure generating chamber 2, as shown in FIG. 7, whereas theentire inner portions of the nozzle 7 and the ink supply aperture 6(FIG. 4) of the first embodiment are tapered, and also in that thetapering angle is set to 15 to 45 degrees in place of 10 degrees ormore.

In the nozzle 7 a and the ink supply aperture 6 a of the secondembodiment, the opening diameter is set to 30 μm, the length of thestraight portions 71 b and 61 b is set to 10 μm, the total length is setto 70 μm, and the tapering angle is set to 25 degrees so as to adjustthe inertance of each component to 0.44×10⁸ kg/m⁴. Hence, if theinertance (0.56×10⁸ kg/m⁴) of the pressure generating chamber 2 isadded, then the inertance m_(T) of the entire passage diameter will be1.43×10⁸ kg/m⁴, which is a value of the upper limit value (1.5×10⁸kg/m⁴) or less of the inertance m_(T) of the entire passage diameterobtained from FIG. 6. The optimum value of the tapering angle depends onthe length of the straight portions, the nozzle diameter, the nozzlelength, etc. as mentioned above. However, considering an optimum nozzleopening diameter, the strength of a nozzle, the prevention of involvingair bubbles, etc., the optimum tapering angle will be 15 degrees or moreand 45 degrees or less for a practical shape (the length of the straightportions is about 10 to about 20 μm).

Next, adjusting the ink viscosity at an environmental temperature of 35°C. to 2.3 mPa·s makes it possible to meet the lower limit value(4.9×10¹² Ns/m⁵) of the acoustic resistance r_(T) at the inertancem_(T)=1.5×10⁸ kg/m⁴ of the entire passage diameter, and this will be theoptimum ink viscosity at a highest temperature (35° C.). Hence, the inkviscosity at a lowest temperature (10° C.) will be 4.8 mPa·s.Furthermore, the ink viscosity at room temperature (20° C.) will beabout 3.5 mPa·s, and the acoustic resistance r_(T) will be 7.3×10¹²Ns/m⁵.

Thus, the target refilling time (100 μs) can be secured and theovershoot can be restrained (10 μm or less) at the same time over theentire apparatus operating temperature range by setting the openingdiameters of the nozzle 7 a and the ink supply aperture 6 a to 30 μm,the length of the straight portions 71 b and 61 b thereof to 10 μm, thetapering angles thereof to 25 degrees, and the ink viscosity tosubstantially 3.5 mPa·s (20° C.).

Since the nozzle 7 a and the ink supply aperture 6 a are provided withthe straight portions 7 b and 61 b, the variations in the openingdiameter in the manufacture can be reduced, thus permitting thevariations in the characteristics of nozzles or heads to be restrained.

The actually implemented evaluation of the refilling characteristics ofthe ink-jet recording head according to the second embodiment has proventhat the refilling time was 96 μs and the overshoot amount was 2.5 μm atthe lowest temperature (10° C.), while the refilling time was 62 μs andthe overshoot amount was 9.8 μm at the highest temperature (35° C.). Inother words, it has been possible to confirm that stable operation canbe performed at the target drive frequency (10 kHz) without causingexcessive overshoot over the entire apparatus operating temperaturerange.

THIRD EMBODIMENT

FIG. 8 is a sectional view showing the shape of a nozzle (an ink supplyaperture has the same shape) that is a third embodiment of the presentinvention.

The third embodiment is characterized in that the diameters of thenozzle 7 b and the ink supply aperture 6 b gradually increase toward thepressure generating chamber 2, the longitudinal sections of the nozzle 7b and the ink supply aperture 6 b have a round shape havingsubstantially equal radius to the length of the nozzle 7 b and the inksupply aperture 6 b, and the length of the nozzle 7 b and the ink supplyaperture 6 b is set to 50 to 100 μm (preferably 70 to 100 μm).

The nozzle 7 b and the ink supply aperture 6 b in this example areprepared by electrocasting (electroforming).

In the nozzle 7 b and the ink supply aperture 6 b of this example, theopening diameter is set to 30 μm and the length is set to 70 μm, and theinertances thereof are both 0.44×10⁸ kg/m⁴. Hence, if the inertance(0.56×10⁸ kg/m⁴) of the pressure generating chamber 2 is added, then theinertance m_(T) of the entire passage system will be 1.43×10⁸ kg/m⁴,which is a value of the upper limit value or less of the inertance m_(T)of the entire passage system, as is obvious from FIG. 6. When theopening diameter of the nozzle is set to 25 to 32 μm, the nozzle lengthmust be set to 100 μm or less in order to obtain a required inertance.

Next, adjusting the ink viscosity at an environmental temperature of 35°C. to 2.2 mPa·s makes it possible to meet the lower limit value(4.9×10¹² Ns/m⁵) of the acoustic resistance r_(T) at the inertancem_(T)=1.5×10⁸ kg/m⁴ of the entire passage diameter, and this will be theoptimum ink viscosity at a highest temperature (35° C.). Hence, the inkviscosity at a lowest temperature (10° C.) will be 2.1 times theviscosity at the highest temperature, i.e., 4.6 mPa·s. The acousticresistance r_(T) at that time will be 10.0×10¹² Ns/m⁵. This is the upperlimit value or less of the acoustic resistance r_(T), and the targetrefilling time can be secured even at the lowest temperature. In thiscase, the ink viscosity at room temperature (20° C.) will be about 3.3mPa·s, and the acoustic resistance r_(T) at that time will be 7.2×10¹²Ns/m⁵.

Thus, the target refilling time (100 μs) can be secured and theovershoot can be restrained (10 μm or less) at the same time over theentire apparatus operating temperature range by forming the nozzle 7 band the ink supply aperture 6 b such that their opening diameter is 30μm, and they are shaped to have radii and a length of 70 μm, and bysetting the ink viscosity to approximately 3.3 mPa·s (20° C.).

The actually implemented evaluation of the refilling characteristics ofthe ink-jet recording head according to the third embodiment has proventhat the refilling time was 98 μs and the overshoot amount was 2.0 μm atthe lowest temperature (10° C.), while the refilling time was 65 μs andthe overshoot amount was 9.6 μm at the highest temperature (35° C.). Inother words, it has been possible to confirm that stable operation canbe performed at a target drive frequency (10 kHz) without causingexcessive overshoot over the entire apparatus operating temperaturerange.

Thus, the embodiments in accordance with the present invention have beendescribed in detail in conjunction with the drawings. Specificconstructions, however, are not limited to the embodiments, andmodifications or the like in design within a scope of the spirit of thepresent invention will be included in the present invention. Forexample, the shapes of the nozzle and the ink supply aperture are notlimited to the taper shape or the radius shape. Similarly, the shape ofthe opening is not limited to the round shape, and it may alternativelybe a rectangular, triangular, or other shape. The ink supply passage formoving the ink pooled in a common ink supply chamber to a pressuregenerating chamber is not limited to the ink supply aperture drilled inthe plate, and it may alternatively be a cylindrical or tubular inksupply passage. Furthermore, the positional relationship among thenozzle, the pressure generating chamber, and the ink supply aperture isnot limited to the structure shown in this embodiment. For example, itis of course possible to dispose the nozzle at the central part or thelike of the pressure generating chamber.

In the embodiments described above, the nozzle 7 and the ink supplyaperture 6 sharing the same shape have been used, but they do not haveto share the same shape, and the ink supply aperture may have any shape.The ink supply aperture does not have much limitation in its diameter orlength, so that it has a higher degree of freedom in its shape ascompared with the nozzle. For instance, if the ink supply aperture has astraight shape (zero-degree tapering angle) with a diameter of 45 μm andhas a length of 70 μm, it is still possible to obtain the inertance of0.44×10⁸ kg/m⁴, which is the target in the first embodiment describedabove.

In the foregoing embodiments, although the inertance of the ink supplyaperture has been set to the same value as that of the nozzle, thepresent invention is not limited thereto. From the viewpoint ofdischarging efficiency, the inertance of the nozzle 7 is preferably setto be smaller than the inertance of the ink supply aperture 6 as long asthe target inertance is obtained in the entire passage diameter. This isbecause, if the inertance of the nozzle 7 is larger than that of the inksupply aperture 6, then the amount of the energy of the pressure wavethat escapes to the ink supply aperture 6 increases, resulting in lowerdischarging efficiency. However, for the convenience of manufacture, theinertances of both may be set to substantially equal values, asdescribed in the foregoing embodiments.

In the foregoing embodiments, the cases have been described where thepresent invention has been applied to the Caesar-type ink-jet recordinghead, The application of the present invention, however, is not limitedto the Caesar-type ink-jet recording head as long as it is an ink-jetrecording head adapted to discharge ink droplets from a nozzle bycausing a change in pressure in a pressure generating chamber by apressure generating means.

Similarly, in addition to a piezoelectric actuator, another type ofelectromechanical transducing element, a magnetostrictive element, or anelectro-thermal converting element may be used as a pressure generatingmeans.

INDUSTRIAL APPLICABILITY

As explained above, the construction in accordance with the presentinvention makes it possible to always secure a target refilling time(approximately 100 μs) and control overshoot to approximately 10 μm orless even if the environmental temperature changes in a range of about10 to about 35° C. when an apparatus is in operation. Therefore, highaccuracy and stability can be secured for ink droplet diameters evenwhen the apparatus is operated at high speed. This enables ink-jetgray-scale recording at high speed with high image quality (by dropletdiameter modulation) to be achieved.

What is claimed is:
 1. An ink-jet recording head comprising a pressuregenerating chamber to be filled with ink, pressure generating means forgenerating a pressure in said pressure generating chamber, an ink supplychamber for supplying the ink to said pressure generating chamber, anink supply passage for establishing communication between said inksupply chamber and said pressure generating chamber, and a nozzle incommunication with said pressure generating chamber, said pressuregenerating means causing a pressure change to take place in said airpressure generating chamber so as to discharge an ink droplet from saidnozzle; wherein the configurations of said nozzle, said ink supplypassage, and said pressure generating chamber are set so that a totalsum m_(T) of inertance and a total sum r_(T) of acoustic resistance (thevalues at a temperature of general 20° C.) of said nozzle, said inksupply passage, and said pressure generating chamber in an ink-filledstate satisfy expressions (1) and (2), respectively:0<m_(T)<1.9×10⁸[kg/m⁴]  (1) 4.0×10¹²<r_(T)<11.0×10¹²[Ns/m⁵]  (2)
 2. Anink-jet recording head according to claim 1, wherein said nozzle has atapered portion whose diameter gradually increases toward said pressuregenerating chamber, and the tapering angle of said tapered portion is 10to 45 degrees.
 3. An ink-jet recording head according to claim 2,wherein the opening diameter of said nozzle is 25 to 32 μm.
 4. Anink-jet recording apparatus comprising said ink-jet recording headaccording to claim
 2. 5. An ink-jet recording head according to claim 1,wherein said nozzle is composed of a straight portion provided in thevicinity of an opening and a tapered portion that gradually increasestoward said pressure generating chamber, and the tapering angle of saidtapered portion is 15 to 45 degrees.
 6. An ink-jet recording headaccording to claim 5, wherein the opening diameter of said nozzle is 25to 32 μm.
 7. An ink-jet recording apparatus comprising said ink-jetrecording head according to claim
 5. 8. An ink-jet recording headaccording to claim 1, wherein the diameter of said nozzle graduallyincreases toward said pressure generating chamber, the longitudinalsection of said nozzle is shaped into a curve that has a radiussubstantially equal to the length of said nozzle, and the length of saidnozzle is 50 to 100 μm.
 9. An ink-jet recording head according to claim8, wherein the opening diameter of said nozzle is 25 to 32 μm.
 10. Anink-jet recording apparatus comprising said ink-jet recording headaccording to claim
 8. 11. An ink-jet recording head according to claim1, wherein the opening diameter of said nozzle is 25 to 32 μm.
 12. Anink-jet recording apparatus comprising said ink-jet recording headaccording to claim
 11. 13. An ink-jet recording head according to claim1, wherein said ink supply passage is an ink supply aperture forestablishing communication between said ink supply chamber and saidpressure generating chamber.
 14. An ink-jet recording apparatuscomprising said ink-jet recording head according to claim
 6. 15. Anink-jet recording head according to claim 1, wherein a maximum dropletdiameter of the ink droplet is set to 38 to 43 μm.
 16. An ink-jetrecording apparatus comprising said ink-jet recording head according toclaim
 15. 17. An ink-jet recording head according to claim 1, whereinsaid ink-jet recording head employs an ink with its surface tension setto 25 to 35 mN/m.
 18. An ink-jet recording head described in claim 1,wherein said ink-jet recording head employs an ink having its viscosityset such that the total sum r_(T) of the acoustic resistance (the valueat a temperature of substantially 20° C.) of said nozzle, said inksupply passage, and said pressure generating chamber in an ink-filledstate satisfies expression (3): 4.0×10¹²<r_(T)<11.0×10¹²[Ns/m⁵]  (3) 19.An ink-jet recording head according to claim 1, comprising a laminatedplate constructed by bonding a nozzle plate wherein said nozzle has beendrilled, a pool plate wherein a space portion of said ink supply chamberis formed, a supply aperture plate wherein said ink supply passage hasbeen drilled, a pressure generating chamber plate wherein a spaceportion of said pressure generating chamber has been formed, and avibrating plate constituting a part of said pressure generating means,and a piezoelectric actuator acting other part of said pressuregenerating means bonded to said laminated plate.
 20. An ink-jetrecording apparatus comprising said ink-jet recording head according toclaim 1.